ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  moan GIF version

Theorem moan 2075
Description: "At most one" is still the case when a conjunct is added. (Contributed by NM, 22-Apr-1995.)
Assertion
Ref Expression
moan (∃*𝑥𝜑 → ∃*𝑥(𝜓𝜑))

Proof of Theorem moan
StepHypRef Expression
1 simpr 109 . 2 ((𝜓𝜑) → 𝜑)
21moimi 2071 1 (∃*𝑥𝜑 → ∃*𝑥(𝜓𝜑))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  ∃*wmo 2007
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515
This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-eu 2009  df-mo 2010
This theorem is referenced by:  moani  2076  mooran1  2078  mormo  2668  rmoan  2912
  Copyright terms: Public domain W3C validator